<?xml version="1.0" encoding="ascii"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
          "DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
  <title>dadi.Hessian</title>
  <link rel="stylesheet" href="epydoc.css" type="text/css" />
  <script type="text/javascript" src="epydoc.js"></script>
</head>

<body bgcolor="white" text="black" link="blue" vlink="#204080"
      alink="#204080">
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
       bgcolor="#a0c0ff" cellspacing="0">
  <tr valign="middle">

  <!-- Tree link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="module-tree.html">Trees</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Index link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="identifier-index.html">Indices</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Help link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="help.html">Help</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Project homepage -->
      <th class="navbar" align="right" width="100%">
        <table border="0" cellpadding="0" cellspacing="0">
          <tr><th class="navbar" align="center"
            ><a class="navbar" target="_top" href="http://dadi.googlecode.com">dadi</a></th>
          </tr></table></th>
  </tr>
</table>
<table width="100%" cellpadding="0" cellspacing="0">
  <tr valign="top">
    <td width="100%">
      <span class="breadcrumbs">
        <a href="dadi-module.html">Package&nbsp;dadi</a> ::
        Module&nbsp;Hessian
      </span>
    </td>
    <td>
      <table cellpadding="0" cellspacing="0">
        <!-- hide/show private -->
        <tr><td align="right"><span class="options">[<a href="javascript:void(0);" class="privatelink"
    onclick="toggle_private();">hide&nbsp;private</a>]</span></td></tr>
        <tr><td align="right"><span class="options"
            >[<a href="frames.html" target="_top">frames</a
            >]&nbsp;|&nbsp;<a href="dadi.Hessian-pysrc.html"
            target="_top">no&nbsp;frames</a>]</span></td></tr>
      </table>
    </td>
  </tr>
</table>
<h1 class="epydoc">Source Code for <a href="dadi.Hessian-module.html">Module dadi.Hessian</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno"> 1</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">logging</tt> </tt>
<a name="L2"></a><tt class="py-lineno"> 2</tt>  <tt class="py-line"><tt id="link-0" class="py-name" targets="Variable dadi.Hessian.logger=dadi.Hessian-module.html#logger,Variable dadi.Inference.logger=dadi.Inference-module.html#logger,Variable dadi.Integration.logger=dadi.Integration-module.html#logger,Variable dadi.Numerics.logger=dadi.Numerics-module.html#logger,Variable dadi.RunInParallel.logger=dadi.RunInParallel-module.html#logger,Variable dadi.Spectrum_mod.logger=dadi.Spectrum_mod-module.html#logger"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-0', 'logger', 'link-0');">logger</a></tt> <tt class="py-op">=</tt> <tt class="py-name">logging</tt><tt class="py-op">.</tt><tt class="py-name">getLogger</tt><tt class="py-op">(</tt><tt class="py-string">'Hessian'</tt><tt class="py-op">)</tt> </tt>
<a name="L3"></a><tt class="py-lineno"> 3</tt>  <tt class="py-line"> </tt>
<a name="L4"></a><tt class="py-lineno"> 4</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">numpy</tt> </tt>
<a name="L5"></a><tt class="py-lineno"> 5</tt>  <tt class="py-line"> </tt>
<a name="hessian_elem"></a><div id="hessian_elem-def"><a name="L6"></a><tt class="py-lineno"> 6</tt> <a class="py-toggle" href="#" id="hessian_elem-toggle" onclick="return toggle('hessian_elem');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Hessian-module.html#hessian_elem">hessian_elem</a><tt class="py-op">(</tt><tt class="py-param">func</tt><tt class="py-op">,</tt> <tt class="py-param">f0</tt><tt class="py-op">,</tt> <tt class="py-param">params</tt><tt class="py-op">,</tt> <tt class="py-param">i</tt><tt class="py-op">,</tt> <tt class="py-param">j</tt><tt class="py-op">,</tt> <tt class="py-param">hi</tt><tt class="py-op">,</tt> <tt class="py-param">hj</tt><tt class="py-op">,</tt> <tt class="py-param">args</tt><tt class="py-op">=</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="hessian_elem-collapsed" style="display:none;" pad="++" indent="++++"></div><div id="hessian_elem-expanded"><a name="L7"></a><tt class="py-lineno"> 7</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L8"></a><tt class="py-lineno"> 8</tt>  <tt class="py-line"><tt class="py-docstring">    Second partial derivative of func w.r.t. parameters i and j</tt> </tt>
<a name="L9"></a><tt class="py-lineno"> 9</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L10"></a><tt class="py-lineno">10</tt>  <tt class="py-line"><tt class="py-docstring">    f0: Value of the function at params</tt> </tt>
<a name="L11"></a><tt class="py-lineno">11</tt>  <tt class="py-line"><tt class="py-docstring">    eps: Stepsize to use</tt> </tt>
<a name="L12"></a><tt class="py-lineno">12</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L13"></a><tt class="py-lineno">13</tt>  <tt class="py-line">    <tt class="py-name">origPi</tt><tt class="py-op">,</tt> <tt class="py-name">origPj</tt> <tt class="py-op">=</tt> <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> </tt>
<a name="L14"></a><tt class="py-lineno">14</tt>  <tt class="py-line"> </tt>
<a name="L15"></a><tt class="py-lineno">15</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">i</tt> <tt class="py-op">==</tt> <tt class="py-name">j</tt><tt class="py-op">:</tt> </tt>
<a name="L16"></a><tt class="py-lineno">16</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPi</tt> <tt class="py-op">+</tt> <tt class="py-name">hi</tt> </tt>
<a name="L17"></a><tt class="py-lineno">17</tt>  <tt class="py-line">        <tt class="py-name">fp</tt> <tt class="py-op">=</tt> <tt class="py-name">func</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L18"></a><tt class="py-lineno">18</tt>  <tt class="py-line"> </tt>
<a name="L19"></a><tt class="py-lineno">19</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPi</tt> <tt class="py-op">-</tt> <tt class="py-name">hi</tt> </tt>
<a name="L20"></a><tt class="py-lineno">20</tt>  <tt class="py-line">        <tt class="py-name">fm</tt> <tt class="py-op">=</tt> <tt class="py-name">func</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L21"></a><tt class="py-lineno">21</tt>  <tt class="py-line"> </tt>
<a name="L22"></a><tt class="py-lineno">22</tt>  <tt class="py-line">        <tt class="py-name">element</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">fp</tt> <tt class="py-op">-</tt> <tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">f0</tt> <tt class="py-op">+</tt> <tt class="py-name">fm</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-name">hi</tt><tt class="py-op">**</tt><tt class="py-number">2</tt> </tt>
<a name="L23"></a><tt class="py-lineno">23</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L24"></a><tt class="py-lineno">24</tt>  <tt class="py-line">        <tt class="py-comment"># f(xi + hi, xj + h)</tt> </tt>
<a name="L25"></a><tt class="py-lineno">25</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPi</tt> <tt class="py-op">+</tt> <tt class="py-name">hi</tt> </tt>
<a name="L26"></a><tt class="py-lineno">26</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPj</tt> <tt class="py-op">+</tt> <tt class="py-name">hj</tt> </tt>
<a name="L27"></a><tt class="py-lineno">27</tt>  <tt class="py-line">        <tt class="py-name">fpp</tt> <tt class="py-op">=</tt> <tt class="py-name">func</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L28"></a><tt class="py-lineno">28</tt>  <tt class="py-line"> </tt>
<a name="L29"></a><tt class="py-lineno">29</tt>  <tt class="py-line">        <tt class="py-comment"># f(xi + hi, xj - hj)</tt> </tt>
<a name="L30"></a><tt class="py-lineno">30</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPi</tt> <tt class="py-op">+</tt> <tt class="py-name">hi</tt> </tt>
<a name="L31"></a><tt class="py-lineno">31</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPj</tt> <tt class="py-op">-</tt> <tt class="py-name">hj</tt> </tt>
<a name="L32"></a><tt class="py-lineno">32</tt>  <tt class="py-line">        <tt class="py-name">fpm</tt> <tt class="py-op">=</tt> <tt class="py-name">func</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L33"></a><tt class="py-lineno">33</tt>  <tt class="py-line"> </tt>
<a name="L34"></a><tt class="py-lineno">34</tt>  <tt class="py-line">        <tt class="py-comment"># f(xi - hi, xj + hj)</tt> </tt>
<a name="L35"></a><tt class="py-lineno">35</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPi</tt> <tt class="py-op">-</tt> <tt class="py-name">hi</tt> </tt>
<a name="L36"></a><tt class="py-lineno">36</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPj</tt> <tt class="py-op">+</tt> <tt class="py-name">hj</tt> </tt>
<a name="L37"></a><tt class="py-lineno">37</tt>  <tt class="py-line">        <tt class="py-name">fmp</tt> <tt class="py-op">=</tt> <tt class="py-name">func</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L38"></a><tt class="py-lineno">38</tt>  <tt class="py-line"> </tt>
<a name="L39"></a><tt class="py-lineno">39</tt>  <tt class="py-line">        <tt class="py-comment"># f(xi - hi, xj - hj)</tt> </tt>
<a name="L40"></a><tt class="py-lineno">40</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPi</tt> <tt class="py-op">-</tt> <tt class="py-name">hi</tt> </tt>
<a name="L41"></a><tt class="py-lineno">41</tt>  <tt class="py-line">        <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPj</tt> <tt class="py-op">-</tt> <tt class="py-name">hj</tt> </tt>
<a name="L42"></a><tt class="py-lineno">42</tt>  <tt class="py-line">        <tt class="py-name">fmm</tt> <tt class="py-op">=</tt> <tt class="py-name">func</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L43"></a><tt class="py-lineno">43</tt>  <tt class="py-line"> </tt>
<a name="L44"></a><tt class="py-lineno">44</tt>  <tt class="py-line">        <tt class="py-name">element</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">fpp</tt> <tt class="py-op">-</tt> <tt class="py-name">fpm</tt> <tt class="py-op">-</tt> <tt class="py-name">fmp</tt> <tt class="py-op">+</tt> <tt class="py-name">fmm</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">4</tt> <tt class="py-op">*</tt> <tt class="py-name">hi</tt> <tt class="py-op">*</tt> <tt class="py-name">hj</tt><tt class="py-op">)</tt> </tt>
<a name="L45"></a><tt class="py-lineno">45</tt>  <tt class="py-line"> </tt>
<a name="L46"></a><tt class="py-lineno">46</tt>  <tt class="py-line">    <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">params</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">origPi</tt><tt class="py-op">,</tt> <tt class="py-name">origPj</tt> </tt>
<a name="L47"></a><tt class="py-lineno">47</tt>  <tt class="py-line"> </tt>
<a name="L48"></a><tt class="py-lineno">48</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">element</tt> </tt>
</div><a name="L49"></a><tt class="py-lineno">49</tt>  <tt class="py-line"> </tt>
<a name="hessian"></a><div id="hessian-def"><a name="L50"></a><tt class="py-lineno">50</tt> <a class="py-toggle" href="#" id="hessian-toggle" onclick="return toggle('hessian');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Hessian-module.html#hessian">hessian</a><tt class="py-op">(</tt><tt class="py-param">func</tt><tt class="py-op">,</tt> <tt class="py-param">params</tt><tt class="py-op">,</tt> <tt class="py-param">eps</tt><tt class="py-op">,</tt> <tt class="py-param">args</tt><tt class="py-op">=</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="hessian-collapsed" style="display:none;" pad="++" indent="++++"></div><div id="hessian-expanded"><a name="L51"></a><tt class="py-lineno">51</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L52"></a><tt class="py-lineno">52</tt>  <tt class="py-line"><tt class="py-docstring">    Matrix of second partial derivatives of func. Hij = dfunc/(dp_i dp_j).</tt> </tt>
<a name="L53"></a><tt class="py-lineno">53</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L54"></a><tt class="py-lineno">54</tt>  <tt class="py-line"><tt class="py-docstring">    func: Function to work with. This function should take params as its first</tt> </tt>
<a name="L55"></a><tt class="py-lineno">55</tt>  <tt class="py-line"><tt class="py-docstring">          argument, and then any number of *args. It will often be convenient</tt> </tt>
<a name="L56"></a><tt class="py-lineno">56</tt>  <tt class="py-line"><tt class="py-docstring">          to use lambda to define the appropriate function.</tt> </tt>
<a name="L57"></a><tt class="py-lineno">57</tt>  <tt class="py-line"><tt class="py-docstring">    params: Parameter values to take derivatives about.</tt> </tt>
<a name="L58"></a><tt class="py-lineno">58</tt>  <tt class="py-line"><tt class="py-docstring">    eps: Stepsize to use. This can be a vector, giving the size for each param.</tt> </tt>
<a name="L59"></a><tt class="py-lineno">59</tt>  <tt class="py-line"><tt class="py-docstring">    args: Optional additional arguments to pass to func.</tt> </tt>
<a name="L60"></a><tt class="py-lineno">60</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L61"></a><tt class="py-lineno">61</tt>  <tt class="py-line">    <tt class="py-name">params</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">)</tt> </tt>
<a name="L62"></a><tt class="py-lineno">62</tt>  <tt class="py-line">    <tt class="py-comment"># Convert eps from (possibly) a constant to a vector.</tt> </tt>
<a name="L63"></a><tt class="py-lineno">63</tt>  <tt class="py-line">    <tt class="py-name">eps</tt> <tt class="py-op">=</tt> <tt class="py-name">eps</tt> <tt class="py-op">+</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L64"></a><tt class="py-lineno">64</tt>  <tt class="py-line">    <tt class="py-comment"># compute cost at f(x)</tt> </tt>
<a name="L65"></a><tt class="py-lineno">65</tt>  <tt class="py-line">    <tt class="py-name">f0</tt> <tt class="py-op">=</tt> <tt class="py-name">func</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L66"></a><tt class="py-lineno">66</tt>  <tt class="py-line"> </tt>
<a name="L67"></a><tt class="py-lineno">67</tt>  <tt class="py-line">    <tt class="py-name">hess</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L68"></a><tt class="py-lineno">68</tt>  <tt class="py-line">    <tt class="py-comment"># compute all (numParams*(numParams + 1))/2 unique hessian elements</tt> </tt>
<a name="L69"></a><tt class="py-lineno">69</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">i</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L70"></a><tt class="py-lineno">70</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L71"></a><tt class="py-lineno">71</tt>  <tt class="py-line">            <tt class="py-name">hess</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt id="link-1" class="py-name" targets="Function dadi.Hessian.hessian_elem()=dadi.Hessian-module.html#hessian_elem"><a title="dadi.Hessian.hessian_elem" class="py-name" href="#" onclick="return doclink('link-1', 'hessian_elem', 'link-1');">hessian_elem</a></tt><tt class="py-op">(</tt><tt class="py-name">func</tt><tt class="py-op">,</tt> <tt class="py-name">f0</tt><tt class="py-op">,</tt> <tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-name">i</tt><tt class="py-op">,</tt> <tt class="py-name">j</tt><tt class="py-op">,</tt> </tt>
<a name="L72"></a><tt class="py-lineno">72</tt>  <tt class="py-line">                                      <tt class="py-name">eps</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">eps</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L73"></a><tt class="py-lineno">73</tt>  <tt class="py-line">            <tt class="py-name">hess</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">hess</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt> </tt>
<a name="L74"></a><tt class="py-lineno">74</tt>  <tt class="py-line"> </tt>
<a name="L75"></a><tt class="py-lineno">75</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">hess</tt> </tt>
</div><a name="L76"></a><tt class="py-lineno">76</tt>  <tt class="py-line"> </tt><script type="text/javascript">
<!--
expandto(location.href);
// -->
</script>
</pre>
<br />
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
       bgcolor="#a0c0ff" cellspacing="0">
  <tr valign="middle">

  <!-- Tree link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="module-tree.html">Trees</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Index link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="identifier-index.html">Indices</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Help link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="help.html">Help</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Project homepage -->
      <th class="navbar" align="right" width="100%">
        <table border="0" cellpadding="0" cellspacing="0">
          <tr><th class="navbar" align="center"
            ><a class="navbar" target="_top" href="http://dadi.googlecode.com">dadi</a></th>
          </tr></table></th>
  </tr>
</table>
<table border="0" cellpadding="0" cellspacing="0" width="100%%">
  <tr>
    <td align="left" class="footer">
    <a href="epydoc-log.html">Generated by Epydoc
    3.0.1 on Fri Dec 14 15:16:34 2012</a>
    </td>
    <td align="right" class="footer">
      <a target="mainFrame" href="http://epydoc.sourceforge.net"
        >http://epydoc.sourceforge.net</a>
    </td>
  </tr>
</table>

<script type="text/javascript">
  <!--
  // Private objects are initially displayed (because if
  // javascript is turned off then we want them to be
  // visible); but by default, we want to hide them.  So hide
  // them unless we have a cookie that says to show them.
  checkCookie();
  // -->
</script>
</body>
</html>
